Skip to main content
SpringerLink
Log in

On the Boundedness of Singular Operators in the Sobolev Space

  • Conference paper
IABEM Symposium on Boundary Integral Methods for Nonlinear Problems

  • 152 Accesses

Abstract

In the present talk I give conditions for the boundedness of a singular integral operator with the symbol depending not only on the angular variable θ ∊ S n−1 but also on the space variable x in the Sobolev class H l(R n), l = 1,2,.... It will be shown that the given conditions are precise in a sense.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Maz’ya, V.G. and Haikin, Ju.E. (1969), A note on continuity in L 2 of the singular integral operator, Vestnik Leningrad. Univ., 19, 156–159.

    Google Scholar 

  2. Maz’ya, V.G. and Shaposhnikova, T.O. (1985) Theory of Multipliers in Spaces of Differentiable functions. Pitman, London.

    Google Scholar 

  3. Mikhlin, S.G. and Prössdorf, S. (1980) Singulär Integraloperatoren, Akademie Verlag, Berlin.

    Google Scholar 

  4. Hörmander, L. (1983) The Analysis of Linear Partial Differential Operators, vol.2, Springer Verlag, Berlin-Heidelberg-New York-Tokyo.

    Book  Google Scholar 

  5. Volevich, L.R. and Paneyaeh, B.P. (1965), Some spaces of generalized functions and imbedding theorems, Uspehi Mat. Nauk 20, 3–74.

    MATH  Google Scholar 

  6. Sawyer, E. (1984), Multipliers of Besov adn power-weighted L 2 spaces, Indiana Univ. Math. J. 33, 353–366.

    Article  MathSciNet  MATH  Google Scholar 

  7. Fefferman, C. (1983), The uncertainty principle, Bull. Amer. Math. Soc. 9, 129–206.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Linköping, 58183, Linköping, Sweden

    T. Shaposhnikova

Authors
  1. T. Shaposhnikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Rome III, Rome, Italy

    Luigi Morino

  2. University of Stuttgart, Stuttgart, Germany

    Wolfgang L. Wendland

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Shaposhnikova, T. (1997). On the Boundedness of Singular Operators in the Sobolev Space. In: Morino, L., Wendland, W.L. (eds) IABEM Symposium on Boundary Integral Methods for Nonlinear Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5706-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5706-3_30

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6406-4

  • Online ISBN: 978-94-011-5706-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation